3 peeled red (Spanish) onions, halved and thinly-sliced
1 tsp. sugar or equivalent sugar-substitute
1 Tbsp. Dijon-style mustard
1 tsp. dried thyme
3 cups fat-free, reduced-sodium beef broth
5 cups water
Salt and freshly ground black pepper
6 1-inch thick slices whole-wheat Italian bread
1/4 cup red or brown rice miso
1/3 cup freshly-grated Parmesan cheese (optional)
Heat half the oil in large Dutch oven or pot over medium-high heat. Add the onions, stirring to coat them with oil. Cover tightly, reduce heat to medium low and cook until onions are wilted, about 10 minutes.
Sprinkle the sugar over the onions and stir in. Increase heat and saute until onions are well browned, about 12 minutes, stirring often.
Remove the pot from heat and scrape it to loosen all the browned bits on the bottom. Stir in mustard, thyme, broth and water. Return to high heat and cook until liquid comes to a boil. Reduce the heat, partially cover the pot and simmer until the onions are very soft, 30 to 40 minutes.
Meanwhile, brush bread on both sides with remaining oil. Grill or toast bread in 400 degree oven. Set aside to cool. Cut into rough cubes with a sharp, serrated knife.
Place the miso in a small bowl. Gradually stir in about 1/4 cup of the soup, mixing until well blended. Stir the mixture into the soup. Season to taste with salt and pepper.
Ladle soup into deep bowls. Sprinkle top with toasted bread cubes. Sprinkle 1 scant tablespoon cheese on top (optional).